2013/02/28 by Yun-Da Hsieh, Ying-Jer Kao, A. W. Sandvik · 3 citations
Physics and Astronomy · #cond-mat.stat-mech #cond-mat.soft
paper · pdf · doi:10.1088/1742-5468/2013/09/p09001
published as J. Stat. Mech. (2013) P09001 · 17 pages, 10 figures. v2: higher-order log-corrections taken into account. New value for the transition temperature
arxiv created 2013/06/17 · arxiv updated 2013/10/02
We test an improved finite-size scaling method for reliably extracting the critical temperature T\rm BKT of a Berezinskii-Kosterlitz-Thouless (BKT) transition. Using known single-parameter logarithmic corrections to the spin stiffness ρs at T\rm BKT in combination with the Kosterlitz-Nelson relation between the transition temperature and the stiffness, ρs(T\rm BKT)=2T\rm BKT/π, we define a size dependent transition temperature T\rm BKT(L1,L2) based on a pair of system sizes L1,L2, e.g., L2=2L1. We use Monte Carlo data for the standard two-dimensional classical XY model to demonstrate that this quantity is well behaved and can be reliably extrapolated to the thermodynamic limit using the next expected logarithmic correction beyond the ones included in defining T\rm BKT(L1,L2). For the Monte Carlo calculations we use GPU (graphical processing unit) computing to obtain high-precision data for L up to 512. We find that the sub-leading logarithmic corrections have significant effects on the extrapolation. Our result T\rm BKT=0.8935(1) is several error bars above the previously best estimates of the transition temperature; T\rm BKT ≈ 0.8929. If only the leading log-correction is used, the result is, however, consistent with the lower value, suggesting that previous works have underestimated T\rm BKT because of neglect of sub-leading logarithms. Our method is easy to implement in practice and should be applicable to generic BKT transitions.